Top universities accuse Gordon Brown of jeopardising 800 years of higher education, warning that they could quickly be "brought to their knees" by the government's spending cuts of up to £2.5bn, thereby damaging Britain's ability to recover from recession.

In a withering attack, the leaders of the Russell Group of 20 leading universities say: "It has taken more than 800 years to create one of the world's greatest education systems, and it looks like it will take just six months to bring it to its knees."

Writing in the Guardian, they say: "If government targets these huge cuts on university budgets they will have a ­devastating effect not only on students and staff, but also on our international competitiveness, national economy and ability to recover from recession ... cuts of this magnitude in overall funding will impact on the sustainability of our research and cannot fail to affect even the most outstanding universities."

The group, which includes Warwick, Liverpool and Glasgow universities as well as Oxford and Cambridge, say that ministers have failed to appreciate one of the "jewels in the country's crown".

"Perhaps the prime minister should consider what his international counterparts regard as being priorities … an investment of €11bn in higher education in France ... Germany pumped a total of €18bn into promoting world-class research alongside university education, whilst Barack Obama ploughed an additional $21bn into federal science spending, as well as announcing a decade-long budget doubling $42.6bn for science, technology and energy.

"There seems to be a greater focus on cutting the funding of higher education than almost anything else. The funding of the health service, police and schools are all currently 'protected' – which presumably reflects their perceived importance at the ballot box."

Wendy Piatt, the group's director general, and Michael Arthur, its chair and the vice-chancellor of Leeds University, warn that at least 30 institutions could disappear, and the rest face possible "meltdown".

The intervention comes amid accusations that the cabinet is split over whether to be more open about the need for spending cuts. Ed Balls, Gordon Brown's closest ally and the schools secretary, played down a split, but revealed that last summer he had argued the need to be more upfront.

The cuts to universities, a third of their annual spend, threaten to reduce a "gold standard" system to one that is "silver, bronze or worse", the top universities warn.

Piatt and Arthur said: "Sadly, the UK can no longer claim to be world-leading in many fields of endeavour. What a great shame it would be to undermine one of the few spheres, namely our universities, in which we do actually still excel.

"We live in a world where ideas, innovation and entrepreneurialism are key to prosperity and wellbeing. As bastions of knowledge and creativity, our universities are critical to supporting this agenda for the next 800 years. This is a defining moment in our country's history. If politicians don't act now, they will be faced with meltdown in a sector vital to our national prosperity.

"If government targets these huge cuts on university budgets, they will have a devastating effect not only on students and staff, but also on our international competitiveness, national economy and ability to recover from recession."

Speaking on the Radio 4's Today programme this morning, Arthur said there was little point in ministers saving the schools budget from cuts "if there aren't universities to take [school leavers] in". He said he recognised the government could not protect every area from cuts, but that universities were a "special case".

He said: "I think we accept as a sector that we have to take a share of responsibility, but so far higher education, particularly in the pre-budget report, has been one of the areas that has been singled out and we think that is a big mistake, particularly if we want to drive the economy forwards.

"We are an absolute cornerstone of British society; the part of the engine that drives the economy of the nation. We supply highly-skilled graduates to the knowledge economy and we provide ideas, research and innovation. We do have a special case to make."

In last month's pre-budget report, ministers announced they would slash £600m by 2013. This is on top of £180m the government asked universities to find in "efficiency savings" by 2011, and a further £135m asked for in the same period by Lord Mandelson, the business secretary who is responsible for universities.

The Institute for Fiscal Studies has warned that even deeper cuts of 12.3% over 2011/12 are needed for ministers to achieve their target of halving national debt by 2013. This would mean an extra £1.6bn of cuts to the science and universities budget.

David Lammy, the higher education minister, said the Russell analysis was "as surprising as it is misleading. We currently invest around £15bn in higher education every year. And the fact is that government's teaching and research funding – even after the £180m efficiency savings and the reductions in December's grant letter – will grow between 2009-10 and 2010-11."

He added: "I'm proud there are now more students than ever before in our history attending university. We maintain our commitment to the importance of higher education precisely because we know how essential its success is to opportunity and to our successful future economic growth.

"We are minimising the effect on the frontline by making savings on capital budgets, asking the sector for further efficiency savings and by asking the Higher Education Funding Council for England to look to reduce funding which will not impact on teaching.

"We are absolutely clear that a high quality student experience with excellent teaching is vital to maintaining the world class higher education we enjoy in this country today."

The Tory spokesman on higher education, David Willetts, said he could not promise to reverse the cuts if his party was in power. A Conservative government would encourage universities to reduce overheads by relying more on charitable donations, he said.Steve Smith, president of Universities UK - the umbrella group for vice-chancellors - has said the cut would force universities to deny places to thousands of students. It comes as a review is underway into whether tuition fees, now £3,225 a year, should rise to at least £5,000.